Dimension formulas of modular form spaces with character for Fricke groups

TL;DR

This paper derives explicit dimension formulas for spaces of holomorphic modular forms with character for specific Fricke groups, expanding understanding of their structure and properties.

Contribution

It provides new explicit dimension formulas for modular form spaces with character for Fricke groups and their extensions with Atkin-Lehner involutions.

Findings

Dimension formulas for ^+(N) with character

Dimension formulas for ^*(N) with Atkin-Lehner involutions

Enhanced understanding of modular form spaces for these groups

Abstract

We first obtain the dimension formulas for the spaces of holomorphic modular forms with character for the Fricke group $\Gamma_0^+(N)$, then that for $\Gamma_0^*(N)$ with all Atkin-Lehner involutions added in a particular case.